Affordances: The Geometry of Action

Week 3: Dynamics of Perception & Action

Tehran Davis

Recap: From Time to Possibility

Last week, we saw how Time-to-Contact (\(\tau\)) specifies when an event will happen.

Today, we ask a deeper question:
What can I do?

  • Is that surface walk-on-able?
  • Is that object grasp-able?
  • Is that gap jump-over-able?

Definition of Affordance

“The affordances of the environment are what it offers the animal, what it provides or furnishes, either for good or ill.” — J.J. Gibson (1979, p. 127)

Key Concept: Affordances are properties of the environment taken with reference to the animal.

Subjective or Objective?

Is “climb-ability” a fact about the stairs? Or a fact about me?

Gibson’s Answer

“An affordance is neither an objective property nor a subjective property; or it is both if you like… It cuts across the dichotomy of subjective-objective.”

It is a Relational Property.

Body Scaling

Imagine you are Alice in Wonderland. You drink the potion and shrink to 6 inches tall.

  • The stairs haven’t changed (Physics is constant).
  • But the Affordance has changed.
    • The stairs are no longer “climb-able.”
    • They are now “cliff-like.”

Conclusion: We measure the world in “body-units,” not inches.

The Classic Study: Warren (1984)

Question: When does a step become “unclimbable”?

  • Hypothesis: It depends on your leg length (\(L\)).
  • Experiment:
    • Group A: Short people.
    • Group B: Tall people.
    • Task: Look at stairs of different heights (\(R\)) and judge “Can you climb this without using your hands?”

The Results

If you plot the data in Inches: - Tall people stop at 30 inches. - Short people stop at 24 inches. - The curves are different.

If you plot the data in Ratios (\(R/L\)): - Everyone stops at 0.88. - The curves overlap perfectly.

The Pi Number (\(\\pi\))

In physics, \(\pi\) refers to a dimensionless ratio (like \(C/D\)). In biology, we have “Intrinsic Metrics.”

\[ \pi = \frac{Riser Height (R)}{Leg Length (L)} \]

  • Critical Point (Max): \(R/L = 0.88\)
  • Optimal Point (Easiest): \(R/L = 0.26\)

Mark (1987): Eye Height

How do you know how long your legs are? You don’t look at them.

Hypothesis: Eye Height (\(E\)) specifies Leg Length (\(L\)). If you are standing on 10cm blocks, you feel taller. Does the world look “smaller”?

  • Result: Yes.
  • Adaptation: After walking for 10 minutes, people recalibrate.

Summary: The Geometry of Action

  1. Perception is Relational (Animal-Environment).
  2. The units of perception are Dimensionless Ratios (\(\\pi\) numbers).
  3. We perceive Effectivities (what we can do), not just properties (what things are).

Next Week: Dynamic Touch

Reading: Turvey, M.T. & Carello, C. (1995). Dynamic Touch.

Topic: How does a blind person “see” the sidewalk with a cane? The answer lies in the Inertia Tensor.